Problem: Solve for $x$ and $y$ using elimination. ${-3x+4y = 37}$ ${-4x+5y = 46}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $-3$ ${-12x+16y = 148}$ $12x-15y = -138$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+4y = 37}\thinspace$ to find $x$ ${-3x + 4}{(10)}{= 37}$ $-3x+40 = 37$ $-3x+40{-40} = 37{-40}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-4x+5y = 46}\thinspace$ and get the same answer for $x$ : ${-4x + 5}{(10)}{= 46}$ ${x = 1}$